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This paper provides a brief overview on existing approaches for defining participation factor in modal analysis. We calculated participation factors using different approximations and specific examples, and then compared the obtained results with equations derived from the mode evolution. As a result, the existing methods for determining a state variable participation factor in mode are proved incorrect result for complex eigenvalue case. Modem software applications designed to analyze power system stability deploy old approaches that provide incorrect results of modal analysis and pose risks to the operation of real power systems. To solve this problem we presented a new broadened definition of participation factor that assures correct results for real and complex eigenvalues cases. We used a two-mass mechanics system to validate proposed approach and our findings confirm the proposed participation factor theory.